6533b83afe1ef96bd12a7088

RESEARCH PRODUCT

Rough nonlocal diffusions

Michele CoghiTorstein Nilssen

subject

Statistics and ProbabilityRough pathApplied Mathematics60H05 60H15 60J60 35K55Probability (math.PR)Conditional probabilityMcKean-VlasovNoise (electronics)510Nonlinear systemMathematics - Analysis of PDEsRough paths60H05Modeling and Simulation35K5560H15FOS: MathematicsApplied mathematicsnon-local equationsDiffusion (business)stochastic PDEsMathematics - ProbabilityAnalysis of PDEs (math.AP)Mathematics

description

We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.

yearjournalcountryeditionlanguage
2019-01-01
10.1016/j.spa.2021.07.002http://arxiv.org/abs/1905.07270